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Propositional logic based on the dynamics of disbelief

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Book cover The Logic of Theory Change

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 465))

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Abstract

Gärdenfors' (1984) epistemic modelling of intuitionistic propositional logic interprets propositions as functions from belief states to belief states. In this paper we generalise his approach by including also disbelief, or rejection, as a basic epistemic attitude. Propositions are here defined as ordered pairs of functions on belief states, representing the attitudes of acceptance and rejection, respectively. For this semantics we obtain strong completeness results wrt the constructive logics of Nelson (1949) and Almukdad and Nelson (1984).

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References

  1. P. Gärdenfors, The Dynamics of Belief as a Basis for Logic, Brit. J. Phil. Sci. 35 (1984): 1–10.

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  2. P. Gärdenfors, Knowledge in Flux, MIT Press, Cambridge and London, 1988.

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  3. D. Pearce & G. Wagner, Reasoning with Negative Information, I: Strong Negation in Logic Programs, Berichte der Gruppe Logik, Wissenstheorie und Information 4/1989, Freie Universität Berlin.

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  4. A. Rossdeutscher, Ereignisfilter und-ideale. Zur algebraischen und topologischen Repräsentation der semantischen Leistung der negation und aspektueller Partikeln wie schon und noch, Berichte der Gruppe Logik, Wissenstheorie und Information, 1990, Freie Universität Berlin (to appear).

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  5. D. Nelson, Constructible Falsity, JSL 14 (1949): 16–26.

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  6. A. Almukdad & D. Nelson, Constructible Falsity and Inexact Predicates, JSL 49 (1984): 231–233.

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  7. H. Rasiowa, An Algebraic Approach to Non-Classical Logics, PWN and North-Holland, Warsaw and Amsterdam, 1974.

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Author information

Authors and Affiliations

  1. Institut für Philosophie, Freie Universität Berlin, Habelschwerdter Allee 30, D-1000, Berlin 33

    David Pearce

  2. Institut für Mathematik II, Freie Universität Berlin, Arnimallee 3, D-1000, Berlin 33

    Wolfgang Rautenberg

Authors
  1. David Pearce
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  2. Wolfgang Rautenberg
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André Fuhrmann Michael Morreau

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© 1991 Springer-Verlag Berlin Heidelberg

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Pearce, D., Rautenberg, W. (1991). Propositional logic based on the dynamics of disbelief. In: Fuhrmann, A., Morreau, M. (eds) The Logic of Theory Change. Lecture Notes in Computer Science, vol 465. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018424

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  • DOI: https://doi.org/10.1007/BFb0018424

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53567-6

  • Online ISBN: 978-3-540-46817-2

  • eBook Packages: Springer Book Archive

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